The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X
 0  X  0 X^3+X^2+X X^2 X^2+X X^3+X^2  X  0 X^3+X^2+X X^3 X^3+X^2+X X^3+X^2  X X^3+X^2 X^3+X X^3 X^3 X^2+X X^2+X X^3 X^2+X X^2 X^2  X X^3+X X^2+X
 0  0 X^3+X^2 X^2 X^2 X^3 X^3 X^3+X^2 X^3 X^3+X^2 X^2  0 X^3+X^2 X^2  0 X^3 X^3 X^3+X^2  0 X^3+X^2  0 X^2 X^3+X^2 X^3 X^3 X^3+X^2  0

generates a code of length 27 over Z2[X]/(X^4) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+28x^25+95x^26+266x^27+94x^28+24x^29+1x^30+2x^31+1x^52

The gray image is a linear code over GF(2) with n=216, k=9 and d=100.
This code was found by Heurico 1.16 in 3.81e-009 seconds.